Survey of Various Image Enhancement Techniques in Spatial Domain Using MATLAB

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1 Suvey of Vaious Image Enhancement Techniques in Spatial Domain Using MATLAB Shailenda Singh Negi M.Tech Schola G. B. Pant Engineeing College, Paui Gahwal Uttaahand, India ABSTRACT Image Enhancement is one of the fist steps in Image pocessing. In this technique, the oiginal image is pocessed so that the esultant image is moe suitable than the oiginal fo specific applications i.e. the image is enhanced. Image enhancement is a puely subjective pocessing technique. An image enhancement technique used to pocess images might be excellent fo a peson but the same esult might not be good enough fo anothe. Image enhancement is a cosmetic pocedue i.e. it does not add any exta infomation to the oiginal image. It meely impoves the subjective quality of the images by woing with the existing data. Image enhancement can be done in following two domains: The Spatial domain and The Fequency domain. This pape focuses on spatial domain techniques fo image enhancement, with paticula efeence to point pocessing methods, histogam pocessing and spatial filteing. Keywods Image enhancement, spatial domain, Point pocessing, Histogam pocessing, Neighbohood pocessing, Filtes, Smoothing filtes, and Shapening filtes. Bhumia Gupta Assistant Pofesso G. B. Pant Engineeing College, Paui Gahwal Uttaahand, India INTRODUCTION Image enhancement [8] is used in inceasing the intepetability o peception of infomation in images fo humans and poviding enhanced input fo othe image pocessing applications. Digital image enhancement techniques povide many choices fo impoving and enhancing the visual quality of images. Appopiate choice of such techniques is geatly influenced by the imaging conditions, tas to do and viewing conditions. Thee exist many techniques that can enhance and impove a digital image without spoiling it. The enhancement techniques can be divided into the following categoies and subcategoies. 1.1 Spatial domain methods The tem spatial domain [] means woing in the given space i.e. the image. It implies woing with the pixel values o in othe wods, woing diectly with the aw data. The pixel values ae alteed to achieve desied enhancement. Image enhancement [8] is applied in evey field of science whee images ae undestood and analyzed. Fo example, medical image analysis, satellite image analysis etc. Let (, ) f x y be the oiginal image whee ƒ is the gey level value o intensity 8

2 value and ( xy, ) ae the image co-odinates. Fo an 8-bit image, ƒ can tae values fom 0-55, whee 0 epesents blac, 55 epesents white and all the intemediate values epesent shades of gay. Image enhancement simply means, tansfoming an image ƒ into image g using T. The modified image can be expessed as: g( x, y) T[ f ( x, y)]... (1). Fo all spatial domain [] techniques it is simply T that changes. The above equation can also be witten as: s T()... (). Whee T is the tansfomation that maps a pixel value into a pixel value s. The esults of this tansfomation [8] ae mapped bac into the gay scale ange as we ae hee dealing only with gey scale digital images. So, the esults ae mapped bac into the ange [0, L-1], whee L=, being the numbe of bits in the image being opeated on. Hee we will only conside gay level images. The same methodology can be extended fo the colo images too. A digital gay image has pixel values in the ange of 0 to 55. In this suvey pape basic image enhancement techniques have been discussed with thei mathematical application and undestanding. This suvey pape will povide an undestanding of undelying concepts, along with algoithms and mathematical concepts commonly used fo image enhancement in spatial domain.. POINT PROCESSING In point pocessing [], we wo with single pixels i.e. T is 1 1 opeato. It means that the new value g( x, y) depends on the opeato T and the pesent f ( x, y ). Point pocessing opeations tae the fom of equation (1) and equation (). Figue below shows basic gey level tansfomation cuves. da egions of an image. The negative of gay image can be obtained by using a simple tansfomation given by: s55. (3). Hence when =0, s =55 and when =55, s =0. Thus s ( L 1)... (4). Whee L is the numbe of gay levels. Figue below shows the negation concept. Fig.3 (a): Input image fo Negation 3 (b): Output Negative image. Logaithmic tansfomations (dynamic ange compession) The log tansfomation [8] maps a naow ange of low input gay level values into a wide ange of output values. The invese log tansfomation pefoms the opposite function. Log functions ae paticulaly useful when the input gay level values in an image have an extemely lage ange of values as the log opeato is an excellent compessing function. The geneal equation of log tansfomation is: s clog(1 ).. (5). Whee c is the nomalization constant. Fig.4 (a): Input image fo log function 4(b): Output fom log function.3 Powe-Law tansfomation The basic fomula fo powe law tansfomation [13] is: g( x, y) c f ( x, y).... (6). Fig.: Basic gey level tansfomation cuves.1 Digital Negative Digital Negatives [13] ae useful in many applications. A common example of digital negative is the displaying of an X- ay image. The pixel gay values ae inveted to compute and find the negative of an image i.e. blac in the oiginal image is conveted into white and vice vesa. Digital Negative images ae paticulaly useful fo enhancing white detail embedded in O s c.... (7). Hee c and ae positive constants. This tansfomation function is also called as gamma coection since is also called as the gamma coection facto. Fo vaious values of diffeent levels of enhancement can be obtained. Non lineaity s encounteed duing image captuing, pinting and displaying can be coected using gamma coection. Hence gamma coection is impotant if the image is to be displayed on the compute sceen. The powe law 9

3 tansfomation can be used to impove the dynamic ange of an image. The minute diffeence between the log tansfomation and the powe law tansfomation is that by using the powe law tansfomation function a lage family of possible tansfomation cuves can be obtained just by vaying the. l * a s m*( a) va b n*( b) wb L 1.. (8). As is evident fom the figue above and by using the above fomula, we mae the da gey levels dae by assigning a slope of less than one and mae the bight gey levels bighte by assigning a slope geate than one. Fig.7 (a): Input image fo contast stetching 7(b): Output image afte contast stetching Fig.5 (a): Input image Fig. 5(b) and 5(c): Output image fo =0.5 and Piecewise-linea tansfomation functions Instead of using a well defined mathematical function we can use abitay use defined tansfoms [8]. The pincipal advantage of piecewise linea functions ove the above types of functions is that the fom of piecewise functions can be abitaily complex. The main disadvantage of piecewiselinea tansfomation functions is that thei specification equies moe use input. Following ae the thee appoaches unde this tansfomation..4.1 Contast Stetching We get low contast images because of insufficient illumination, lac of dynamic ange in the image sensos and wong setting of a lens apetue duing image acquisition. Contast stetching [8][14] is a pocess that expands the ange of intensity levels in an image so that it spans the full intensity ange of the ecoding medium o display device. The eason behind this is to incease the contast of the images by maing the da potions dae and the bight potions bighte. The figue below shows the tansfomation used to achieve contast stetching. Fig.6: Contast stetching cuve One can assign diffeent slopes depending on the input image and the application. As we now that image enhancement is a subjective technique and hence thee is no set of slope values that would yield the desied esult. The contast stetching tansfomation inceases the dynamic ange of the modified image. Fom the above gaph we can see that the location of (, s ) and (, s) points 1 1 contol the shape of the tansfomation function. If 1 s1 and s, the tansfomation is a linea function that poduces no changes in intensity levels. If 1, s1 0 and s L 1, the tansfomation becomes a theshold function [5] that ceates a binay image as shown below. The geneal equation fo theshold image is 0 sl if a. s if aand 1 Fig.8 (a): Thesholding function 8(b): Theshold image fo fig.7 (a) (, s ) and (, s ) poduce Intemediate values of 1 1 vaious degees of spead in the intensity levels of the output image. In geneal 1 and s1 s is assumed, so that the function is single valued and monotonically inceasing. This condition peseves the ode of intensity levels, thus peventing the ceation of intensity atifacts in the pocessed image..4. Intensity (gay) level slicing Gay level slicing [8] is the spatial domain equivalent to bandpass filteing in the fequency domain. A gey level slicing function can eithe, highlight a goup of intensities and diminish all othes o it can highlight a goup of intensities 10

4 and leave the est alone. Applications include enhancing featues such as masses of wate in satellite imagey and enhancing flaws in X-ay images. The tansfomation function loos simila to the theshold function except that hee we select a band of gey level values. It is of following two types: gey level slicing without bacgound and gey level slicing with bacgound Gay level slicing without bacgound This can be implemented using the below fomulation: sl1 if a b and s 0, othewise. This method is called as gey level slicing without bacgound [13]. This is because in this pocess, we have completely lost the bacgound. and 8 is the numbe of bits equied to epesent each pixel. 8 8 bits simply means o 56 gey levels. In bit plane slicing, we see the impotance of each bit in the final image. The highe ode bits contain majoity of the visually significant data, while the lowe ode bits contain less details. It is also used in Steganogaphy [10], which is the at of hiding infomation. Fig.9 (a): Gey level without bacgound function 9(b): Output image.4.. Gay level slicing with bacgound In some applications, thee is a need to enhance a band of gey levels as well as to etain the bacgound. This technique of etaining the bacgound is called as gey level slicing with bacgound [13]. This can be implemented by using the fomula below: sl 1 if a b and s, othewise. Fig.10 (a): Gey level with bacgound function 10(b): Output image.4.3 Bit plane slicing Pixels ae digital numbes composed of bits. Fo example, the intensity o gey level value of each pixel in a 56-level geyscale is composed of 8 bits. Instead of showing intensity level anges, we could highlight the contibution made to total image appeaance by specific bits. An 8-bit image may be consideed as being composed of eight 1-bit planes, with plane 1 containing the lowest-ode bit of all pixels in the image and plane 8 all the highest-ode bits. Decomposing an image into its bit planes is useful fo analyzing the elative impotance of each bit in the image. Also, this ind of decomposition into bit planes is useful fo image compession [8]. Let an image is defined as an image. In this, is the total numbe of pixels in the image Fig.11 (a): Input image 11(b): Image fomed with LSB and 11(c): Image fomed with MSB 3. HISTOGRAM PROCESSING Histogam [] of images povides a global desciption of the appeaance of an image. Histogam of an image epesents the elative fequency of occuence of the vaious gey levels in an image. Just by looing at the histogam of an image, a geat deal of infomation can be obtained. It can be plotted in two ways. It can be plotted in two ways. In the fist case, the x-axis has the gey levels and the y-axis has the numbe of pixels in each gey level i.e. h( ) n... (9), whee = th intensity value and n = numbe of pixels in the image with intensity. In the second case, the x-axis has the gey levels and the y-axis has the pobability of the occuence of that gey level i.e. p( ) n / MN.... (10), fo =1, L-1, whee M and N ae the ow and column dimensions of the image. This is nown as nomalized histogam. The advantage of this method is that the maximum value to be plotted will always be Histogam Stetching It is a technique used to incease the dynamic ange [11] of an image. In this method, we do not change the basic shape of the oiginal histogam, but we spead it to the entie dynamic ange. We achieve this by using a staight line equation as shown. s T ( ) m( ) s.. (11), min min m s s /. max Whee max min max min = maximum 11

5 gey level of input image, min = minimum gey level of input image, s max = maximum gey level of output image, s min = minimum gey level of output image. This tansfomation function shifts and stetches the gey level ange of the input image to occupy the entie dynamic ( s, s ). Figue below explains this thing clealy. ange min max Fig.1 (a): Oiginal Image 1(b): Oiginal Image Histogam Fig.13 (a): Pocessed image 13(b): Pocessed image histogam 3. Histogam Equalization Thee ae many applications, wheein we need a flat histogam; this cannot be achieved by histogam stetching [1]. A pefect image is one which has equal numbe of pixels in all its gey levels. Hence ou objective is not only to spead the dynamic ange, but also to have equal pixels in all the gey levels. This is called as histogam equalization [1]. So we need a tansfomation that would tansfom a bad histogam to a flat histogam. The tansfomation that we need must satisfy the below two conditions. We now s T() fo 0 1. (a) T () Must be single valued and stictly monotonically inceasing function in the inteval 0 1. (b) 0 T ( ) 1 Fo 0 1i.e. 0s 1fo 0 1, hee the ange of is taen as [0, 1]. This is called the nomalized ange [8]. This ange is taen fo simplicity. Since the tansfomation is single valued and monotonically inceasing, the invese tansfomation exists. i.e. T 1 () s ;0s 1. The gey levels fo continuous vaiables can be chaacteized by thei pobability density function p () and ps () s. Fom pobability theoy we now that if p () and T () ae nown and if T 1 () s satisfies condition (a), then the pobability density of the tansfomed gey level is ps( s) [ p( ) d / ds]. (1). T 1 ( s) we now need to find a tansfomation which would give us a flat histogam. Let us conside the cumulative density function (CDF) [11]. CDF is obtained by simply adding up all the PDF. i.e. s T( ) p ( ) d ;0 1 0,. (13). ds Diffeentiating with espect to, we get p () d. Hence ps ( s) [1] 1; 0s 1. This is nothing but a unifom density function. A bad histogam becomes a flat histogam when we find the CDF. Fo discete values, we deal with pobabilities and summations instead of PDFs and integals. Thus n p () MN... (14), fo =0, 1,..L-1, whee MN=total numbe of pixels in the image, n = numbe of pixels that have intensity. The discete fom of the tansfomation is ( L 1) s T ( ) ( L 1) p ( j ) = n j MN (15), j0 j 0 fo =0, 1,..L-1. Thus a pocessed image is obtained by mapping each pixel in the input image with intensity into a coesponding pixel with level s in the output image using above equation. The example given below explains this pocedue. Fig.14 (a): Oiginal image 14(b): Oiginal image Histogam Fig. 15 (a): Equalized image 15(b): Equalized image histogam 1

6 3.3 Histogam Specification (Matching) Histogam equalization [11] automatically detemines a tansfomation function that sees to poduce an output image that has a unifom histogam. It is not inteactive, i.e., it always gives one esult-an appoximation to a unifom histogam. It is at times desiable to have an inteactive method in which cetain gey levels ae highlighted. In paticula, it is useful some times to be able to specify the shape of the histogam that we wish the pocessed image o output image to have. The method used to geneate a pocessed image that has a specified histogam [13] is called histogam matching o histogam specification. Let and z ae continuous intensities and let p () and pz ( z) denote thei coesponding continuous PDFs, espectively. Hee and z denote the intensity levels of the input and output images espectively. We can estimate p () fom the given input image, while pz ( z) is the specified pobability density function that we wish the output image to have. Let s be a andom vaiable with the popety: s T( ) ( L 1) p ( w) dw o (16), whee w is a dummy vaiable of integation. Suppose z be a andom vaiable with the popety z G( z) ( L 1) p ( t) dt s o z.. (17), whee t is a dummy vaiable of integation. It then follows fom these two equations that G( z) T( ) and, theefoe, that z must satisfy the condition 1 1 z G T G s [ ( )] ( ). (18). the equations (16), (17), (18) above show that an image whose intensity levels have a specified PDF can be obtained fom a given image by using the following pocedue. (a) Find the histogam p () of the input image and detemine its equalization tansfomation using equation (16). (b) Use the specified PDF p ( ) z z of the output image to obtain the tansfomation function using equation (17). (c) Find the invese tansfomation z G 1 () s ; because z is obtained fom s, this pocess is a mapping fom s to z, the latte being the desied values. (d) Obtain the output image by equalizing the input image fist; the pixel values in this image ae the s values. Then fo each pixel in the equalized image [8], pefom the invese mapping to obtain the coesponding pixel of the output image. Histogam matching [11] enables us to match the gey scale distibution in one image to the gey scale distibution in anothe image. The discete fomulation fo histogam matching [11] is shown below. The discete fomulation of equation (16) is s T ( ) ( L 1) p ( ) = j j0 ( L 1) n j MN j 0... (19), fo =0, 1,..L-1. Similaly, given a specific value of s, the discete fomulation of equation (17) involves computing the tansfomation function q G( z ) ( L 1) p ( z ) q z i i0 fo a value of q, so that 1 ( q) ( ).. (0), G z G s... (1). Thus, it pefoms a mapping fom s to z. We may summaize the histogam-specification pocedue fo discete case as follows: - (a) Find the histogam p () of the given image and use it to find the histogam equalization tansfomation. Round off the esulting values of s to the intege ange [0, L- 1]. (b) Compute all values of the tansfomation function G fo q=0, 1,.L-1, whee p ( z ) ae the values of the specified histogam. Round off the values of G to integes in the ange [0, L-1]. Stoe the values of G in a table. (c) Fo evey value of s, =0, 1,.L-1. Use the stoed values of G fom pevious step to find the coesponding value of zq so that Gz ( q ) is closest to s and stoe these mappings fom s to z. when moe than one values of z satisfies the given s, choose the smallest value by q convention. (d) Fom the histogam-specified image by fist histogam-equalizing the input image and then mapping evey equalized pixel value, s of this image to the coesponding value z in the histogam-specified image using the mappings q found in step (c). 4. NEIGHBOURHOOD PROCESSING OR SPATIAL FILTERING The name filte [13] is taen fom fequency domain pocessing, whee filteing efes to accepting (passing) o ejecting cetain fequency components. A filte that passes low fequencies is called a low pass filte [13]. The net effect poduced by a low pass filte is to blu (smooth) an image. We can obtain a simila smoothing diectly on the image itself by using spatial filtes. A spatial filte consists of (a) A neighbouhood (b) A pedefined opeation that is pefomed on the image pixels encompassed by the neighbouhood. Filteing [] ceates a new pixel with co-odinates equal to the co-odinates of the cente of the neighbouhood, and whose value is the esult of the filteing opeation. A pocessed image is geneated as the cente of the filte visits each pixel in the input image. If the opeation pefomed on the input image pixels is linea, then the filte applied is called as a linea spatial filte. Othewise, the filte is non-linea []. 4.1 Smoothing Spatial Filtes Smoothing filtes ae basically used fo bluing and fo eduction of noise in images. Bluing is used in pepocessing tass, such as emoval of fine details fom an image pio to object extaction and vaious othe applications, and bidging of small gaps in lines o cuves. z i 13

7 Noise eduction can be accomplished by bluing with a linea filte and also by non-linea filte Smoothing Linea Filtes The output of a smoothing, linea spatial filte [13] is simply the aveage of the pixels contained in the neighbouhood of the filte mas. These filtes sometimes ae called aveaging filtes, they ae also called as low pass filtes. Aveaging filtes [] wo on the pincipal of eplacing the value of evey pixel in an image by the aveage of the intensity levels in the neighbouhood defined by the mas. This pocess esults in an image with educed shap tansitions in intensities. Since andom noise shows shap tansitions in intensity levels, the most obvious application of smoothing is Gaussian noise eduction. Howeve edges also ae chaacteized by shap intensity tansitions, so aveaging filtes have the undesiable side effect that they blu edges along with noise eduction. Aveaging filtes wos well fo Gaussian and salt noise but fails fo peppe noise. Figue below shows two common 33filtes. Fig.16 (a): Aveaging Filte 16(b): Weighted Aveaging Filte Use of the fist filte gives the standad aveage of the pixels unde the mas. A m nmas would have a nomalizing constant equal to 1 nm. The second mas gives us a weighted aveage of the pixels unde its neighbohood. In this mas the cente of the mas s pixel is multiplied by a highe value than any othe, thus giving this pixel moe impotance in the calculation of the aveage. The main motive behind weighing the cente point the highest and then educing the value of the coefficients as a function of inceasing distance fom the oigin is simply an effot to educe bluing in the smoothing pocess. The geneal implementation fo filteing an MN image with a weighted aveaging filte of size m nis given by Fig.18: Output of fig.17 (a) and (b) afte applying aveaging filte Fig.19: Output of fig.17 (a) and (b) on applying weighted aveaging filte 4.1. Ode-Static (non Linea) filtes The esponse o esult of these filtes depends on odeing (aning) the pixels contained in the image aea encompassed by the filte o mas, and then eplacing the value of the cente pixel with the value detemined by the aning opeation esult. Median filte [], max filte [] and min filte [] fall unde this categoy. Median filte eplaces the value of a pixel by the median of the intensity values in the neighbohood of that pixel. Median filtes ae vey effective in the emoval of salt and peppe noise (impulsive noise) because of its appeaance as white and blac dots supeimposed on an image. The median opeato equies an odeing of the values in the pixel neighbohood at evey pixel location. This inceases the computational cost of the median opeato. g( x, y) a b sa tb a w( s, t) f ( x s, y t).. (), b sa tb w( s, t) fo x=0, 1,..M-1, y=0, 1, N-1. The images below show the esult of both the above mas. Fig.0 (a): Image with Gaussian noise 0(b): Image with Salt and peppe noise Fig.17 (a): Image with Gaussian noise 17(b): Image with Salt and peppe noise Fig.1 (a): Output of Median filte on Gaussian noise 1(b): Output of Median filte on salt and peppe noise 14

8 4. Shapening Spatial filtes The main objective of shapening filtes is to highlight tansitions in intensity. Shapening [] can be accomplished by spatial diffeentiation [6]. The deivatives of a digital function [] ae defined in tems of diffeences. We equie that any definition we use fo a fist deivative must be- (a) (b) (c) Zeo in aea of constant intensity. Non zeo at the onset of an intensity step o amp. Non zeo along amps. Similaly, any definition of a second deivative must be- (a) (b) (c) Zeo in aeas of constant intensity. Non zeo at the onset and end of an intensity step o amp. Zeo along amps of constant slope. Fig. 4(a): and 4(b): Output on applying Laplacian filte The Laplacian This is the simplest isotopic filte [13], whose esponse is independent of the diection of the discontinuities in the image. It is defined fo a function (image) f ( x, y) of two vaiables as f x f y f... (3). Because deivatives of any ode ae linea opeations, the laplacian is a linea opeato. To expess this equation in discete fom, we have f f ( x 1, y) f ( x 1, y) f ( x, y)... (4). x f (5). f ( x, y 1) f ( x, y 1) f ( x, y) y Theefoe, discete laplacian of two vaiables is as below: f ( x, y) f ( x 1, y) f ( x 1, y) f ( x, y 1) f ( x, y 1) 4 f ( x, y)..(6). this equation can be implemented using the filte mas (a) shown below. It gives an isotopic esult fo otations in incements of 90 degee. Filte mas (b) is used to implement isotopic esults in incements of 45 degee. Thei implementation on images is shown below. Fig. 5(a): and 5(b): Output on applying Laplacian filte Since the laplacian [15] is a deivative opeato, its usage highlights intensity discontinuities in an image and deemphasizes egions with slowly vaying intensity levels. This will esult in images with gayish edge lines and othe discontinuities poducing featueless bacgound. Bacgound featues can be ecoveed while still peseving the shapening effect of the laplacian simply by adding the laplacian image to the oiginal image. The basic ways in which we use the laplacian fo image shapening is given by g( x, y) f ( x, y) c[ f ( x, y)].. (7), whee f ( x, y) and g( x, y) ae the input and shapened images espectively. The constant c=-1, if the above two laplacian filtes ae used and c=1 if the above laplacian filtes coefficient ae multiplied by -1. Fig. (a): Laplacian filte 1 (b): Laplacian filte Fig.6 (a): and 6(b): Input images fo Shapening Fig.3: Input images to both the above filtes Fig. 7(a) and (b): Images afte applying laplacian filte 15

9 Fom these equations filte mass ae developed. Robets use g z z and g z9 z6. The coss diffeences:- x 9 5 x gadient image using above two gadients is M ( x, y) [( z z ) ( z z ) ].... (33). Fom equation (30), 1/ M( x, y) z z z z Fig. 8 (a) and (b) shapened Image afte adding Images of Fig.6 (a) with 7 (a) and fig.6 (b) with 7 (b) The patial deivative tems used in above equation can be implemented using the two linea filte mass below. 4.. The Gadient Fist deivatives in image pocessing ae implemented using the magnitude of the gadient [1]. Fo f ( x, y ), the gadient of f at coodinates ( xy, ) is defined as the D column vecto given by f... (8). gx x f gad( f ) g f y y this vecto points in the diection of the geatest ate of change of f at location ( xy, ). The magnitude of vecto f, denoted as M( x, y) is the value at ( xy, ) of the ate of change in the diection of the gadient vecto and is as M ( x, y) mag( f ) gx g y... (9). M( x, y) is an image of the same size as the oiginal and is also called as the gadient image. Because the components of the gadient vecto ae deivatives, they ae linea opeatos. Howeve, the magnitude of this vecto is not because of the squaing and squae oot opeations. On the othe hand, the patial deivatives [] in eq. (8) ae not otation invaiant (isotopic), but the magnitude of the gadient vecto is. Equation (9) can be witten as M( x, y) gx g... (30). y We now define discete appoximations to the above equations using the matix shown below. Fig.30 (a): and (b): Robets gadient using coss diffeence Fig.31 (a): Input image (b): Output image fom Robets mas Pewitts 3 3mas depends on following gadients. f gx ( z7 z8 z9) ( z1 z z3) x. (34). f g y ( z3 z6 z9) ( z1 z4 z7)..... (35). y The gadient image using above two gadients is M( x, y) ( z z z ) ( z z z ) ( z z z ) ( z z z ) (36) The patial deivative tems used in above equation can be implemented using the two linea filte mass below. Fig.9: Matix epesentation fo pixels in an image Discete appoximations to the above equations ae: - f gx f ( x 1, y) f ( x, y) z z x 8 5 f g y f ( x, y 1) f ( x, y) z z y 6 5. (31).. (3). Fig.3 (a): Pewitts x-gadient (b): Pewitts y-gadient 16

10 Fig.33 (a): Input image 33(b): Output image on applying Pewitts mas Sobel33mas depends on following gadients. f gx ( z7 z8 z9) ( z1 z z3)... (37). x f g y ( z3 z6 z9) ( z1 z4 z7)... (38). y The gadient image using above two gadients is M( x, y) ( z z z ) ( z z z ) ( z z z ) ( z z z ). (39) The patial deivative tems used in above equation can be implemented using the two linea filte mass below. Fig.34 (a): Sobel x-gadient 34(b): Sobel y-gadient Fig.35 (a): Input image 35(b): Output image on applying Sobel mas Implementation of Robets [3], Pewitts [3] and Sobel [3] opeatos on the image can be done in two steps. (a) Add the x and y gadient into one gadient mas. (b) Convolve [11] the new mas with the oiginal image. 5. CONCLUSION Image enhancement [8] algoithms offe an enomous vaiety of appoaches fo modifying images to obtain visually acceptable images. The choice of specific methodology is a function of the specific tas as an application, content of an image, obseve featues, and viewing conditions. The suvey of vaious Image enhancement techniques in spatial domain has been successfully accomplished using matlab code on two images Penguin.jpg and Sachin.jpg in this pape. Image Enhancement is one of the most impotant and difficult component of digital image pocessing. Based on the type of image and type of noise with which it is coupted, a slight change in individual method o combination of any methods futhe impoves visual quality. In this pape, we focus on studying the existing techniques of image enhancement in spatial domain. The point pocessing methods ae an impotant image pocessing techniques and ae used basically fo contast enhancement. Digital Negative is suited and is used fo enhancing white detail embedded in da egions. It has applications in medical imaging. Powe-law functions ae useful fo geneal pupose contast manipulation applications. Fo a da image with histogam towads the dae egion, an expansion of gay levels is obtained using a powe-law tansfomation with a factional exponent less than 1. Log Tansfomation is beneficial fo expessing and enhancing details in the dae egions of the image at the expense of detail in the bighte egions. Fo an image having a washedout o bighte appeaance, a compession of gay levels is obtained using a powe-law tansfomation with gamma geate than 1. The histogam of an image (i.e., a plot of the gay level fequencies) povides impotant infomation egading the contast of an image though the intensity values in an image. Histogam equalization is a tansfomation that stetches the contast by edistibuting the gay-level values unifomly without poducing a flat histogam. Only the global histogam equalization can be done completely automatically. Although in this suvey pape we did not discuss the computational cost of enhancement algoithms. it may play an impotant and citical ole in the selection of an algoithm fo eal-time applications. Despite the effectiveness of each of these techniques when applied sepaately, in pactice one has to devise a combination of such methods to achieve moe effective image enhancement. 6. REFERENCES [1] A. K. Jain, Fundamentals of Digital Image Pocessing, Pentice Hall of India, [] Rafael C. Gonzalez and Richad E. woods, Digital Image Pocessing, Peason Education, Second Edition, 005. [3] W. K. Patt, Digital image pocessing, Pentice Hall, [4] Gajanand Gupta, Algoithm fo Image Pocessing Using Impoved Median Filte and Compaison of Mean, Median and Impoved Median Filte, Intenational Jounal of Soft Computing and Engineeing (IJSCE) ISSN: , Volume-1, Issue-5, Novembe 011. [5] Chis Solomon, Fundamentals of Digital Image Pocessing, John Wiley & Sons Ltd. [6] R. Jain, R. Kastui and B.G. Schunc, Image Pocessing Fundamentals, McGaw-Hill Intenational Edition, [7] Jafa Ramadhan Mohammed, An Impoved Median Filte Based on Efficient Noise Detection fo High Quality Image Restoation, IEEE Int. Conf, PP , May 008. [8] Raman Maini and Himanshu Aggawal A Compehensive Review of Image Enhancement Techniques, Jounal of Computing, Volume, Issue 3, Mach 010, pp

11 [9] Sunita Dhaiwal, Compaative Analysis of Vaious Image Enhancement Techniques, Intenational Jounal of Electonics & Communication Technology (IJECT), Vol., Issue 3, pp , Sept [10] Bhabatosh Chanda and Dwijest Dutta Majumde, 00, Digital Image Pocessing and Analysis. [11] R.W.J. Wees, (1996). Fundamental of Electonic Image Pocessing. Bellingham: SPIE Pess. [1] R Hummel, Histogam modification techniques, Compute gaphics and Image Pocessing, Vol. 4, pp. 09-4, [13] Dhananjay K. Thecedath, 008. Digital Image Pocessing. Tech -Max publication, Pune, India. [14] Balvant Singh, Ravi Shana Misha, Puan Gou, Analysis of Contast Enhancement Techniques fo undewate image, Intenational Jounal of Compute Technology and Electonics Engineeing (IJCTEE) ISSN: , Vol. 1, Issue, pp [15] Asst. Pof. D. Umut Aioz, Lectue notes on Digital Image pocessing, Lectue 3: Image enhancement in Spatial Domain. 18